Structure and stability of bent core liquid crystal fibers.

Recently it was found that fluid smectic phases of bent core liquid crystals formed freestanding fibers of extremely high slenderness ratios. Studies of these fibers showed that their structure was composed of concentric cylindrical smectic layers. For this configuration to be stable there must be an energy term that desires bending of the smectic layers. We show that an energy term that deals with the divergence of the dipolar direction can encourage layer bending if the layer chirality value is allowed to vary. The energy term associated with holding the layer chirality is closely related to layer compressions and electrical self-interactions. For our model, we assumed a simple smectic-C geometry with constant molecular tilt and cone angle defined by the director with respect to the layer normal, but allowed a constant variation of the polar direction about the director. Applying this simplified model to a free energy which accounts for director distortions, divergence of the polar direction, biaxial layer strain, surface tension, and electrical self-interactions, we were able to show consistency between the stable fiber radius and other properties predicted in our model to results from experimental studies.

Electric-field-induced nematic-cholesteric transition and three-dimensional director structures in homeotropic cells.

We study the phase diagram of director structures in cholesteric liquid crystals of negative dielectric anisotropy in homeotropic cells of thickness d which is smaller than the cholesteric pitch p. The basic control parameters are the frustration ratio d/p and the applied voltage U. Upon increasing U, the direct transition from completely unwound homeotropic structure to the translationally invariant configuration (TIC) with uniform in-plane twist is observed at small d/p < or = 0.5. Cholesteric fingers that can be either isolated or arranged periodically occur at 0.5 < or = d/p<1 and at the intermediate U between the homeotropic unwound and TIC structures. The phase boundaries are also shifted by (1) rubbing of homeotropic substrates that produces small deviations from the vertical alignment; (2) particles that become nucleation centers for cholesteric fingers; (3) voltage driving schemes. A novel reentrant behavior of TIC is observed in the rubbed cells with frustration ratios 0.6 < or = d/p < or = 0.75, which disappears with adding nucleation sites or using modulated voltages. In addition, fluorescence confocal polarizing microscopy (FCPM) allows us to directly and unambiguously determine the three-dimensional director structures. For the cells with strictly vertical alignment, FCPM confirms the director models of the vertical cross sections of four types of fingers previously either obtained by computer simulations or proposed using symmetry considerations. For rubbed homeotropic substrates, only two types of fingers are observed, which tend to align along the rubbing direction. Finally, the new means of control are of importance for potential applications of the cholesteric structures, such as switchable gratings based on periodically arranged fingers and eyewear with tunable transparency based on TIC.

Geometrical optics approach in liquid crystal films with three-dimensional director variations.

A formal geometrical optics approach (GOA) to the optics of nematic liquid crystals whose optic axis (director) varies in more than one dimension is described. The GOA is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example, the GOA is applied to the calculation of light transmittance for the case of a liquid crystal cell which exhibits the homeotropic to multidomainlike transition (HMD cell). Properties of the GOA solution are explored, and comparison with the Jones calculus solution is also made. For variations on a smaller scale, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating light transmittance. The results of light transmittance calculations for the HMD cell based on the director patterns provided by two methods, direct computer calculation and a previously developed simplified model, are in good agreement.

Asymmetric transmissive behavior of liquid-crystal diffraction gratings.

We have used computer simulations to predict that the beam-steering efficiency of a common liquid-crystal diffraction grating will depend on which side is presented to the incident beam. The finite-difference time-domain method and the Helmholtz-Kirchhoff diffraction integral were utilized to simulate the performance of an idealized configuration of the grating.